{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BBAAAAAAAcByBBAAAAAAAcByBBAAAAAAAcByBBAAAAAAAcFxBBBI/+tGPdOCBByoQCOj1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\nrrWNQHmFn2RIPpYKydtEP0833CCNGuXuKgAAuCwTfbKi2qU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x265192c9c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 产生一个随机数\n",
    "rng = np.random.RandomState(1)\n",
    "X = np.sort(10 * rng.rand(80, 1), axis=0)\n",
    "y = np.sin(X).ravel()\n",
    "y[::5] += 3 * (0.5 - rng.rand(16))\n",
    "#构建不同深度的决策树\n",
    "clf_0 = DecisionTreeRegressor(max_depth=1)\n",
    "clf_1 = DecisionTreeRegressor(max_depth=2)\n",
    "clf_2 = DecisionTreeRegressor(max_depth=3)\n",
    "clf_3 = DecisionTreeRegressor(max_depth=4)\n",
    "clf_0.fit(X, y)\n",
    "clf_1.fit(X, y)\n",
    "clf_2.fit(X, y)\n",
    "clf_3.fit(X, y)\n",
    "#创建预测模拟数据\n",
    "X_test = np.arange(0.0, 10, 0.01)[:, np.newaxis]\n",
    "y_0 = clf_0.predict(X_test)\n",
    "y_1 = clf_1.predict(X_test)\n",
    "y_2 = clf_2.predict(X_test)\n",
    "y_3 = clf_3.predict(X_test)\n",
    "#图表展示\n",
    "plt.figure(figsize=(16,9),dpi=80,facecolor='w')\n",
    "plt.scatter(X, y, c=\"k\", s=10,label=\"data\")\n",
    "plt.plot(X_test, y_0, c=\"y\", label=\"max_depth=1,$R^2$=%.3f%%\" % (clf_0.score(X, y)), linewidth=2)\n",
    "plt.plot(X_test, y_1, c=\"g\", label=\"max_depth=2,$R^2$=%.3f%%\" % (clf_1.score(X, y)), linewidth=2)\n",
    "plt.plot(X_test, y_2, c=\"r\", label=\"max_depth=3,$R^2$=%.3f%%\" % (clf_2.score(X, y)), linewidth=2)\n",
    "plt.plot(X_test, y_3, c=\"b\", label=\"max_depth=5,$R^2$=%.3f%%\" % (clf_3.score(X, y)), linewidth=2)\n",
    "plt.xlabel(\"X\", horizontalalignment=\"left\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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